4D Theory Research Articles

Cardy limits of 6d superconformal theories

We explore the supersymmetric partition functions of 6d SCFTs on ℝ4 × T2 with non-vanishing charges for compatible global symmetries. We utilize the elliptic genera for self-dual strings and compute the free energy of 6d SCFTs in the Cardy limit. For a 6d (2,0) theory on N M5-brane, we obtain the free energy proportional to N3. We find that the origin of N3 comes from the condensation of the self-dual strings, whose total number is proportional to frac{N^3-N}{6} . We further extend our analysis to the general E-string theory and obtain its Cardy free energy.

Factorised 3d mathcal{N} = 4 orthosymplectic quivers

We study the moduli space of 3d mathcal{N} = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d mathcal{N} = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

Can effective four-dimensional scalar theory be asymptotically free in a spacetime with extra dimensions?

We trace what happens with asymptotically free behavior of the running coupling in $\phi^{3}$ theory in six-dimensional space-time if to compactify two spatial dimensions on a 2D closed manifold. The result can be considered as an effective 4D theory of infinitely many KK-type scalar fields with triple interactions. The effective \emph{dimensional} coupling inherits running to zero at high mass scales in a modified form depending on the size of the compact manifold. Some physical implications are discussed.

Observations on BPS observables in 6D

We study possible geometries and R-symmetry breaking patterns that lead to globally BPS surface operators in the six dimensional theory. We find four main classes of solutions in different subspaces of and a multitude of subclasses and specific examples. We prove that these constructions lead to supersymmetry preserving observables and count the number of preserved supercharges. We discuss the underlying geometry, calculate their anomalies and present analogous structures for the holographic dual M2-branes in AdS 7 × S 4. We also comment on the dimensional reduction of these observables to line and surface operators in 4D and 5D theories. This rich spectrum of operators is proposed as the simplest and most natural observables of this mysterious theory.

H(4) tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts

The use of lattice tensor representations is explored to investigate the lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge theory in 4D. The analysis of several tensor bases allows to quantify the completeness of the various tensor bases considered, the deviations of the lattice results from the continuum theory due to the lattice artefacts and estimate the theoretical uncertainty in the propagator. Furthermore, our analysis tests continuum based relations with the lattice data and show that the lattice Landau gauge gluon propagator is described by a unique form factor, as in the continuum formulation.

Do all 5d SCFTs descend from 6d SCFTs?

We present examples of 5d SCFTs that serve as counter-examples to a recently actively studied conjecture according to which it should be possible to obtain all 5d SCFTs by integrating out BPS particles from 6d SCFTs compactified on a circle. We further observe that it is possible to obtain these 5d SCFTs from 6d SCFTs if one allows integrating out BPS strings as well. Based on this observation, we propose a revised version of the conjecture according to which it should be possible to obtain all 5d SCFTs by integrating out both BPS particles and BPS strings from 6d SCFTs compactified on a circle. We describe a general procedure to integrate out BPS strings from a 5d theory once a geometric description of the 5d theory is given. We also discuss the consequences of the revised conjecture for the classification program of 5d SCFTs.

Bootstrapping BPS spectra of 5d/6d field theories

We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup hat{mathrm{mathbb{C}}} 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d mathcal{N} = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

4d mathcal{N} = 2 SCFTs and lisse W-algebras

We continue our studies of the correspondence between 4d mathcal{N} = 2 SCFTs and 2d W-algebras. The purpose of this paper is to study the relationship between 2d lisse W-algebras and their 4d SCFT partners. The lisse W-algebra is the W-algebra whose associated Zhu’s C2 algebra is finite dimensional. As the associated variety of Zhu’s C2 algebra is identified with the Higgs branch in the 4d/2d correspondence, the lisse condition is equivalent to the absence of the Higgs branch on the 4d side. We classify 4d mathcal{N} = 2 SCFTs which do not admit Higgs branch, then these theories would give lisse W-algebras through the 4d/2d correspondence. In particular, we predict the existence of a large class of new non-admissible lisse W-algebras, which have not been studied before. The 4d theories corresponding to lisse W-algebra can appear in the Higgs branches of generic 4d mathcal{N} = 2 SCFTs, therefore they are crucial to understand the Higgs branches of mathcal{N} = 2 SCFTs.

Unitarity in KK-graviton production, a case study in warped extra-dimensions

The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.

W algebras, cosets and VOAs for 4d mathcal{N} = 2 SCFTs from M5 branes

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general mathcal{N} = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

More on holographic correlators: twisted and dimensionally reduced structures

Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d mathcal{N} = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

More on topological vertex formalism for 5-brane webs with O5-plane

We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1]. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO(N) gauge theories and the pure G2 gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level 9. At the end we rewrite the O-vertex in a form of a vertex operator.

Generalized global symmetries of T[M] theories. Part I

We study reductions of 6d theories on a d-dimensional manifold Md, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 −d)-dimensional theory T[Md]. We refine and generalize the notion of “polarization” to polarization on Md, which serves to fix the spectrum of local and extended operators in T[Md]. Another important feature of theories T[Md] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the ’t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.

Character-based 4C Learning Model to Improving Students' Metacognitive Abilities: A Develop Phase of Research & Development

This research aims to determine the level of validity, practicality, and effectiveness (develop phase) development of character-based 4C learning models to improve students' metacognitive abilities. This research focuses on the develop phase of the 4D theory (Define, Design, Develop and Disseminate) by Thiagarajan, Semmel, & Semmel (1974). The develop phase consists of validity testing by experts, practicality testing by lecturers, and effectiveness testing by students. The subjects of this research were 16 students and 2 lecturers of the Primary School Teacher Education Research Program (PGSD) STKIP Andi Matappa, Pangkep Regency. In addition, two validators were also selected as participants to assess the validity of this research product. The data collection techniques used was validation sheet, questionnaire, and tests. The collected data were analyzed using a quantitative approach with the help of SPSS 23.00. The results showed that the research products in the form of model books and character-based 4C learning tools were declared valid, practical, and effective and could be used by lecturers to teach Pancasila and Citizenship Education courses.

Probing compactified extra dimensions with gravitational waves

We study the effect of compact extra dimensions on the gravitational wave luminosity and waveform. We consider a toy model, with a compactified fifth dimension, and matter confined on a brane. We work in the context of five-dimensional (5D) general relativity, though we do make connections with the corresponding Kaluza-Klein effective 4D theory. We show that the luminosity of gravitational waves emitted in 5D gravity by a binary with the same characteristics (same masses and separation distance) as a 4D binary is 20.8% less relative to the 4D case, to leading post-Newtonian order. The phase of the gravitational waveform differs by 26% relative to the 4D case, to leading post-Newtonian order. Such a correction arises mainly due to the coupling between matter and dilaton field in the effective 4D picture and agrees with previous calculations when we set black holes' scalar charges to be those computed from the Kaluza-Klein reduction. The above corrections to the waveform and the luminosity are inconsistent with the gravitational-wave and binary pulsar observations, and they thus effectively rule out the possibility of such a simple compactified higher dimensions scenario. We also comment on how our results change if there are several compactified extra dimensions and show that the discrepancy with 4D general relativity only increases.

Higher-form symmetries of 6d and 5d theories

We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

Entanglement entropy: non-Gaussian states and strong coupling

In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability bonanza shown by these variational ansatze allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the ϕ4 scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

Product SCFTs in class-S

We develop a technique for counting the number of stress tensor multiplets in a 4D mathcal{N} = 2 SCFT. This provides a simple diagnostic for when an isolated (non-Lagrangian) SCFT is a product of two (or more) such theories. In class-S, the basic building blocks are the isolated SCFTs arising from the compactification of a 6D (2,0) theory on a 3-punctured sphere (“fixture”). We apply our technique to determine when a fixture is a product SCFT. The answer is that this phenomenon is surprisingly rare. In the low-rank AN−1, DN theories and the E6 theory studied by the first author and his collaborators, it occurs less than 1% of the time. Of the 2979 fixtures in the (untwisted and twisted) E6 theory, only 23 are product SCFTs. Of these, 22 were known to the original authors. The new one is a product of the (E7)8 Minahan-Nemeschansky theory and a new rank-2 SCFT.

4d F(4) gauged supergravity and black holes of class \u2131

We perform a consistent reduction of 6d matter-coupled F(4) supergravity on a compact Riemann surface {Sigma}_{mathfrak{g}} of genus mathfrak{g} , at the level of the bosonic action. The result is an mathcal{N} = 2 gauged supergravity coupled to two vector multiplets and a single hypermultiplet. The four-dimensional model is holographically dual to the 3d superconformal field theories of class ℱ, describing different brane systems in massive type IIA and IIB wrapped on {Sigma}_{mathfrak{g}} . The naive reduction leads to a non-standard 4d mixed duality frame with both electric and magnetic gauge fields, as well as a massive tensor, that can be only described in the embedding tensor formalism. Upon a chain of electromagnetic dualities, we are able to determine the scalar manifolds and electric gaugings that uniquely specify the model in the standard supergravity frame. We then use the result to construct the first examples of static dyonic black holes in AdS6 and perform a microscopic counting of their entropy via the 5d topologically twisted index. Finally, we show the existence of further subtruncations to the massless sector of the 4d theory, such as the Fayet-Iliopoulos gauged T3 model and minimal gauged supergravity. We are in turn able to find new asymptotically AdS4 solutions, providing predictions for the squashed S3 partition functions and the superconformal and refined twisted indices of class ℱ theories.

Anomaly inflow methods for SCFT constructions in type IIB

We extend the anomaly inflow methods developed in M-theory to SCFTs engineered via D3-branes in type IIB. We show that the ’t Hooft anomalies of such SCFTs can be computed systematically from their geometric definition. Our procedure is tested in several 4d examples and applied to 2d theories obtained by wrapping D3-branes on a Riemann surface. In particular, we show how to analyze half-BPS regular punctures for 4d mathcal{N} = 4 SYM on a Riemann surface. We discuss generalizations of this formalism to type IIB configurations with F3, H3 fluxes, as well as to F-theory setups.